Tapered bore gas burners



July 24, 1956 w. M. DOW ETAL TAPERED BORE GAS BURNERS Filed Feb. 16. 1950 H/Gf/ DEL/VERY TURBULf/VT FLOW LAMINAR F L 0W m T fN w m a m 0 P d r. m r /U 5 k QPCVQ \tuai Dus A TTORNE Y5 TAPERED BORE GAS BURNERS Willard M. Dow and Burnie Porter, Shreveport, La., as-

signors to United Gas Corporation, Shreveport, La., a corporation of Delaware Application February 16, 1950, Serial No. 144,404

2 Claims. (Cl. 158-114) This invention relates to new and useful improvements in pipe burners and methods of constructing the same.

Pipe burners are in general use throughout industry and in their simplest form comprise a length of standard pipe having one end closed and having a row of ports drilled along the top. The gas is introduced through the open end and flows toward the closed or dead end, escaping through the burner ports where the gas is ignited to provide the burner flame. This type of pipe burner has been found relatively satisfactory when employed in shorter lengths but when an attempt is made to employ a pipe burner of considerable length the friction losses due to the flow of gas through the pipe become a major factor and cause certain inherent disadvantages which interfere with the operation and efliciency of the burner.

To produce efficient operation and uniform heating characteristics of a pipe burner, it is desirable that the flame height be substantially uniform at all burner ports throughout the operating range of the burner. Generally, burners have a turndown ratio of three or four to one and in order to produce efficient and uniform heating characteristics, it is necessary that the gas pressure at each burner port be substantially the same as the pressure at all other burner ports at any given or selected gas delivery rate within the operating range of the burner. In other words, at various delivery rates, the flame height, although higher or lower in accordance with a higher or lower rate of delivery, must always be uniform at all burner ports.

It has been found that an elongate pipe burner of any appreciable length and capacity has only a single optimum delivery rate for the production of a uniform flame height and uniform heating throughout the over-all length of the burner; if the delivery rate is increased the flame height and heating will tend to increase toward the dead end of the burner while a decrease in the delivery rate will result in a decrease in flame height and heating toward said dead end. This uneven flame height and heating is a disadvantage which discourages the use of the simple type pipe burner in the longer lengths because it results in low turndown ratios, low capacity, and non-uniform heating characteristics.

As a gas-air mixture is introduced into a pipe burner and flows from the inlet end to the dead end thereof, a pressure drop tends to occur due to the friction losses in the gas-air mixture flow through the pipe. Also a pressure increase due to the deceleration of flow in the pipe which necessarily occurs as portions of the gas escape through the burner ports tends to take place. The pressure loss due to friction is related to the surface area of the pipe while the pressure gain due to deceleration is related to the cross-sectional area of said pipe. When the two pres-sure trends, that is, the pressure drop due to friction loss and the pressure increase due to deceleration, are exactly balanced the gas pressure is constant along the entire length of the burner to thereby assure a uniform flame height and uniform heating. If these two pressure 2,755,85l Patented July 24, 1956 2 trends are not maintained in balance, the flame height and heating becomes variable.

Taking the ordinary cylindrical pipe burner as an example, the gas enters the inlet end of the burner at a predetermined delivery rate and flows through the pipe toward the dead end thereof. As it flows through the pipe a pressure drop occurs due to friction losses and at the same time a pressure increase due to deceleration of flow caused by the gas escaping through the burner ports is also effected. Because the cross-sectional area is constant the two pressure trends do not balance each other throughout the length of the pipe with the result that the flame height varies throughout the length of the burner. At the optimum delivery rate in the usual cylindrical pipe burner, these two pressure trends are balanced and a substantially uniform flame with resultant uniform heating is produced. However, with an increased or high delivery when the Nr rate the flame at the dead end of the pipe will be higher than that at the inlet end because at the higher delivery rate, the kinetic energy or inertia of the flow stream overbalances the friction losses; conversely, at a low delivery rate the flame at the inlet end of the pipe burner is higher than the flame at the dead end of the burner because under such a condition the kinetic energy or inertia is not suflicient to overcome the friction losses. It is, therefore, evident that the normal type of pipe burner has one optimum delivery rate at which rate the burner will function efliciently. At all other delivery rates the flame height and heating are non-uniform.

As a fluid, such as the gas-air mixture in a pipe burner, flows through a closed area there may occur two different types of flow: laminar and turbulent. In the laminar flow the fluid moves in layers or laminas while in turbulent flow there are secondary irregular motions and velocity fluctuations superimposed on the principal or average flow. It is accepted practice to use the dimensionless Reynolds number Nr as a criterion for determining whether the pipe flow with any fluid is laminar or turbulent. A rela tively small Nr indicates that viscous and frictional forces predominate, as in laminar flaw, whereas a relatively large Nr indicates that inertia forces predominate, as in turbulent flow. It has been proven that the stable form of motion for pipe flow is normally laminar where the Reynolds number is less than 2000 and is turbulent where the values of N! are above 2000. This 2000 value is taken merely as an average since it is possible that in certain cases and under various conditions a laminar flow might be maintained above 2000 and also turbulent flow may start at some point below 2000. However, on the average and under usual conditions it may be stated that laminar flow occurs below an Nr of 2000 and turbulent flow occurs at an N1 value above 2000. The Reynolds number is dependent upon the velocity of the fluid and the internal diameter of the flow pipe.

Because of the two types of flow, laminar and turbulent, further difficulty is encountered in attempting to employ an elongate simple type pipe burner having uniform' heating characteristics. As flow changes from turbulent to laminar the friction factor undergoes a substantial change with the result that operation of a burner is seriously affected because there has been no change in internal pipe diameter to compensate for the pressure loss variation which occurs in changing from one type of flow to another. If gas is admitted at a delivery rate and into a pipe burner of a diameter where the Nr is greater than 2000, the flow of the gas entering the pipe burner is turbulent and at some point in said pipe changes to laminar drops below 2000. With a constant diameter pipe burner it is apparent that that portion of the pipe burner wherein laminar flow occurs has different flame and heating characteristics than that portion wherein turbulent flow occurred,

Certain short length pipe burners have employed gradually reduced or tapered internal cross-sectional area but such reductions have always been along a linear taper whereby the cross-sectional area decreases in proportion to the distance from the inlet end. Such a linear taper is effective only when frictional forces are entirely negligible and the manifold pressure is governed by kinetic energy eflects alone. Thus, the linear taper is from a practical standpoint effective only where the flow rate is high and the burner length is short and would not provide for efficiency of operation in an elongate pipe burner of considerably length because it fails to take into consideration pressure drop which would necessarily take place due to frictional loss in a pipe of considerable length. It has been found that where the effective burner length is greater than five times the inlet diameter (twenty times the hydraulic radius of said inlet), the frictional forces become an appreciable factor and the linear taper is ineflective in providing uniform distribution of heat. In view of this, the use of longer length burners utilizing the linear taper would require increased diameters which render them impractical.

Recognizing the inherent disadvantages and limitations of the usual pipe burner, various manufacturers have attempted to control the flame height and heating by controlling the ratio of the cross-sectional area of the pipe to the total burner port area and substantially all burners are now constructed so that the total burner port area is less than the cross-sectional area of the pipe. However, this imposes very severe limitations on the capacity and length of a pipe burner, and consequently greatly limits the utility of this type of burner. This invention allows the capacities of conventional pipe burners to be increased several hundred per cent, because the total port area of the burner may be greatly increased far beyond the crosssectional area of the burner at its inlet end. A typical design of burner constructed in accordance with the present invention provides a total port area which is approximately ten times the cross-sectional area of the burner inlet. As a result, a burner having extremely high capacity relative to its physical dimensions may be produced and in actual practice, a burner constructed as disclosed herein has a capacity of approximately ten times the capacity of conventional burners of the same physical size.

One object of this invention is to provide a gas burner wherein the internal cross-sectional area of the burner manifold is varied in a definite relationship to the internal surface area of said manifold, whereby under any given delivery rate a controlled distribution of the flame height and heating characteristics is produced throughout the length of the burner; such a distribution of the flame height and heating characteristics may be uniform or may be other than uniform but will in any event have a definite and desired relationship to the distance along the burner.

It is another object to provide an improved pipe burner which is so constructed that the pressure drop in the gasair stream due to friction losses in the flow through the pipe is exactly balanced by the pressure increase due to the deceleration of flow in the pipe which necessarily occurs when part of the gas escapes through the port, with such balance being maintained throughout the length of the pipe burner whereby the pressure at all burner ports is substantially equal for any given delivery rate to thereby assure uniform flame height and uniform heating throughout the length of the burner.

An important object of the invention is to provide an improved gas burner wherein the internal cross-sectional area of the burner manifold is varied in a definite relationship to the internal surface area of said manifold, whereby the pressure of the gas-air mixture at each of the burner ports is substantially equal under any given delivery rate whereby uniform flame and heating characteristics are produced throughout the length of the burner.

A particular object of the invention is to provide a burner which is constructed for use in a certain operating range and which has a uniform or other desired flame height at all burner ports under any selected delivery rate within said operating range.

Still another object is to provide an improved burned wherein the cross-sectional area of the burner pipe is varied in accordance with the type of flow of the gas whereby an elongate burner having gas entering the same in the turbulent flow range and then being decelerated into the laminar flow range will have its pressure substantially constant at all of the burner ports throughout the length of the burner at any given delivery rate.

Still another object is to provide a burner constructed of a burner manifold having a constant internal cross-sectional area, together with an insert adapted to be disposed within the pipe for varying the cross-sectional area of said pipe; the insert having a varying cross-sectional area which is constructed in accordance with calculations predicated on a balance of the frictional and kinetic energy forces of the gas stream, whereby high capacity and controlled heating characteristics are obtained.

A still further object is to provide elongate inserts, each of a different cross-sectional contour or profile for insertion into a simple cylindrical pipe burner, whereby the use of the desired insert makes the burner adaptable for efficient use within certain-operating ranges and also whereby the single burner is made extremely flexible and may be readily converted for eflicient operation in different operating ranges.

The construction designed to carry out the invention will be hereinafter described together with other features thereof.

The invention will be more readily understood from a reading of the following specification and by reference to the accompanying drawings forming a part thereof, wherein an example of the invention is shown, and wherein:

Figure l is a longitudinal sectional view of an ordinary cylindrical pipe burner illustrating the flame height under optimum delivery rate conditions,

Figure 2 is a similar view of the burner of Figure 1, showing the flame height under high delivery rates,

Figure 3 is a similar view, illustrating the flame height when the delivery rate is low,

Figure 4 is a longitudinal sectional view of the pipe burner having an improved insert, constructed in accordance with the invention, mounted therein,

Figure 5 is an isometric view of the insert,

Figure 6 is a horizontal cross-sectional view, taken on the line 66 of Figure 4,

Figure 7 is a horizontal cross-sectional view, taken on the line 7-7 of Figure 4,

Figure 8 is a horizontal crosssectional view, taken on the line 8-8 of Figure 4,

Figure 9 .is a longitudinal sectional view of a modified form of the invention, and

Figure 10 is a Reynolds number chart illustrating the variation in the friction factor as it occurs in laminar and turbulent flow.

In the drawings the letter A designates the usual type of pipe burner which includes a cylindrical pipe or manifold it of constant diameter. One end of the pipe is closed by an end cap 11, this end being generally referred to as the dead end of the burner. A conventional primary air inspirator 12 is provided at the inlet end of the pipe and air-gas mixture flows through the pipe in the direction of the arrows in Figure l. A plurality of burner ports 13 which are usually formed in spaced relation to each other through the length of the pipe are drilled in said pipe and as the gas-air mixture escapes upwardly through the ports and is ignited the usual burner flame B is formed. The burner as shown in Figure l is a standard type of pipe burner and it will be apparent that if the pressure at all of the points 13 is constant the height of the burner flame B will be uniform throughout the length of the burner.

In general, the pressure loss in the gas-air stream due to friction as said stream flows through the pipe or manifold is related to the surface area of said pipe or manifold, while the pressure gain in sail stream due to deceleration as the gas-air mixture escapes through ports 13 is related to the cross-sectional area of the pipe or manifold. Thus, at some specific optimum delivery rate the ratio of the internal surface area of the pipe is adjusted to the internal cross-sectional area of said pipe with the result that the pressure drop which occurs due to friction losses in the gas flow through the pipe is exactly balanced by the pressure increase due to the deceleration of flow in the pipe which occurs as a result of the gas escaping through the ports. Under this optimum delivery rate the flame height B will be uniform throughout the length of the burner and uniform heating characteristics will be had, this condition being illustrated in Figure 1.

However, under every delivery rate other than optimum, the flame height and resulting heating are not uniform, and in Figure 2, the flame height which occurs in the burner 10 under a high delivery rate is illustrated. Due to the increased rate of flow the kinetic energy forces of the gas-air stream are greater than the friction losses at the inlet end of the pipe or manifold with the result that the pressure of the gas-air mixture at those ports nearer the inlet end is less than the pressure at the ports nearer the dead end. Because of the difierent pressures at the ports, the flame height at the dead end 11 of the pipe 10 is higher with a gradual reduction in flame height toward that port closest to the inlet end, as indicated in Figure 2.

Similarly, under a low delivery rate which is illustrated in Figure 3 the flame height is also variable but in a manner reverse to the variation in flame height in Figure 2. In this case under the lower delivery rate the pressure drop in the stream due to friction losses is greater than the pressure increase in said stream due to deceleration with the result that the flame height at the inlet end is higher than the flame height at the dead end. It is apparent that as the length of the burner is increased the variations in flame height under all delivery rates except the optimum delivery rate are amplied and for this reason it has been impossible to employ pipe burners of any appreciable length where the pipeburner is constructed of a pipe or manifold having a constant cross-sectional area.

In carrying out the present invention a pipe burner C shown in Figure 4 is provided. Ordinarily, it will be desirable to maintain the height of the burner flame uniform and the invention will be described herein as accomplishing this result; however, in some instances it may be desired to control the distribution of heat by varying the flame height at the different burner ports and the invention contemplates controlling the flame height in any predetermined manner. The burner C may be constructed of a tubular pipe or manifold having one end closed by a cap 21 and having a plurality of burner ports 22 drilled therein. A conventional primary air inspirator 23 is provided at the inlet end of the pipe 20 whereby air and gas may be introduced into the burner. The pipe or manifold of the burner C has its internal cross-sectional area varied throughout its length, or throughout a portion or portions thereof, and this variation in cross-sectional area is preferably accomplished by a generally tapered insert 24 which is removably disposed within the bore 20a of the pipe. It is preferable that the variation in the cross-sectional area of the pipe burner be accomplished by an insert because in this manner the insert may be removed and replaced with another insert of a slightly diflerent contour, whereby the same burner pipe 20 may be employed for operation in different operating ranges.

However, if desired, the burner may be constructed as shown in Figure 9 wherein the burner D comprises a body 25 or manifold having a dead end 26 and inlet end 27. The body is formed with a longitudinal bore 28 extending longitudinally thereof. A portion 29 of the wall of the bore extends parallel to the axis of the body while the remainder 30 of the wall of the bore is generally curved along a predetermined path, as will be explained, to vary the cross-sectional area of the bore 28. Burner ports 31 are formed in that portion 29 of the wall of the body and it will be evident that in this modification the cross-sectional area of the burner is varied longitudinally, just as in the form shown in Figure 4; however, the contoured wall 30 is substituted for the removable insert 24 of Figure 4.

The particular contour of the insert 24 and the contour of the portion 30 of the wall of the bore 28in Figure 5 are constructed in a particular manner and when uniform flame height is to be maintained are designed so that the cross-sectional area of the burner is gradual- 1y changed throughout its length in order to maintain a substantially constant pressure at all of the burner ports under any given delivery rate within the operating range of the burner. The contour or profile of either the insert of Figure 4 or the wall 30 to Figure 9 takes into consideration the turbulent and laminar flow conditions which might occur in the burner and thus the particular burner described herein assures uniform flame height and heating characteristics at all delivery rates throughout the operating range of said burner.

In describing the particular manner by which the crosssectional area of the burner is varied, reference is made to the law of conservation of energy and the law of conservation of matter. The fundamental mathematical statement of the energy balance for the gas flow through the pipe or manifold 20 (Figure 4) or manifold 28 (Figure 9) is: Equation 1; f +%+dr=o where,

u=1inear velocity of gas flowing through pipe du=differential linear velocity c=a dimensionless constant representing flow conditions which is equal to for streamline flow and approximately 1 for turbulant fiow dp=diiferential static pressure of gas s=density of gas 2 (IF =friction= g-dx where f=Fannings friction factor, dx=differential length of burner, D=diameter of pipe burner For the conditions of uniform heating and uniform flame height this equation may be reduced to:

dDD

Equation II: y-cf where the new symbols mean,

dD=diiferential diameter of pipe dy=difierential distance from dead end of pipe y=distance from dead end of pipe Equation IIA:

It is apparent that in order to maintain the pressure substantially constant at all of the burner ports 22 of the burner at any given delivery rate it is necessary to bring about a condition which will insure that the pressure drop due to friction losses in the flow through the pipe or manifold is exactly balanced by the pressure increase due to the deceleration of the flow in the pipe or manifold which occurs when part of the gas escapes through the burner ports. Since the pressure loss due to friction is related to the surface area of the pipe while the pressure gain due to deceleration is related to the cross-sectional area of the pipe, it is at once apparent that by adjusting the ratio of these two areas by controlling the contour of the insert 24 or the wall 30 it is possible to control the pressure of the gas at the burner ports.

Considering first the design where the flow is laminar, that is, where the Reynolds number is less than 2000, the friction factor is inversely proportional to the Reynolds number and Equation II set forth above can be solved mathematically to yield the design equation as follows:

Equation III:

Equation HE: E

1 D- Di let[ [I 2 where the new symbols mean,

If the cross-sectional shape of the burner is not circular, the hydraulic radius may be substituted for diameter in the foregoing equation to yield:

Equation IV:

1 marl,

m= 2 Q an where m=hydraulic radius which is defined as the crosssectional area divided by the wetted perimeter.

From the above it will be evident that the contour of the insert 24 is in accordance with the above calculations where the gas how is in the laminar range, that is, where the Reynolds number is less than 2000. The required cross-sectional area will be calculated at desired longitudinally spaced points throughout the length of the burner and the distance between the points of calculation may be varied Within limits. As indicated in Figure 4, the calculations may be made at points P, P1, P2, P3, P4 and at other desired points throughout the length of the insert. So long as a smooth curve between the points at which the calculations are made is provided the design of the insert will be satisfactory. Positioning of the insert 24 within the pipe or manifold results in varying the internal cross-sectional area of the pipe or manifold and adjusts the cross-sectional area with respect to the internal surface area, whereby an equal pressure is maintained at all burner ports at any given delivery rate within the operating range of the burner.

In the foregoing discussion of the design of the insert 24 or the wall portion 30 it has been assumed that the fluid flow is in the laminar range and referring to Figure 6 this would be in the range R on the chart. The line 32 is representative of the variation in friction factor in the laminar range, such line being relatively steep. When flow is in the turbulent range as indicated by the letter T, the variation in friction factor is considerably less with respect to velocity or rate of flow. Therefore, the equation which controls the design of the insert 24 or wall 30 to vary the cross-sectional area does not apply.

In turbulent flow f (Fannings friction factor) is commonly expressed as a function of the Reynolds number by the following type of equation:

Equation V:

where b and n are numerical constants.

This relationship is shown by line 33 in the chart, Figure 10. Equation II set forth above can now be solved mathematically to yield the design equation for turbulent flow:

Equation VI:

where,

By making the calculations at various spaced points throughout the pipe or manifold length and shaping the contour of profile of the insert 24 or wall 30 in accordance therewith, the internal cross-sectional area of the manifold pipe is varied so as to maintain an equal pressure at all burner ports at any given delivery rate within the operating range and throughout the turbulent flow range. The foregoing Equation VI applies when the pipe is circular in cross-section and in making the calculations for pipes of other cross-sectional shape, four times the hydraulic radius is substituted for the diameter in said equation. As is well known, the hydraulic radius is defined as the cross-sectional area divided by the wetted perimeter.

The calculations will be made along the length of the insert 24 or the wall 30 at the desired spaced intervals to provide the required contour and thus, if the flow through the pipe burner is turbulent as it enters said burner, pressure at all burner ports is maintained equal.

In actual operation the gas-air mixture at the inlet end may be in the turbulent flow range in which case that portion of the insert 24 or wall 30 will be designed inaccordance with the design equation relating to turbulent flow. At some point in the burner the Reynolds number will have decreased to 2000 and from that point on the flow will be laminar. Beyond the point where the Reynolds number has dropped to 2000 and below, the insert 24 and the wall 30 will be designed in accordance with the Equation III relating to laminar flow. It is thus apparent that the invention contemplates a variation in the cross-sectional area of the burner which will maintain a balance of frictional and kinetic energy forces at all times regardless of the type of flow. In other words, the pressure drop in the gas-air mixture due to friction losses in flowing through the pipe is exactly balanced at all times by the pressure increase due to the deceleration of flow in the pipe which occurs as a result of gas escaping through the ports. This pressure balance is maintained irrespective of the type of how and is constant along the entire length of the burner which assures a uniform flame height and uniform heating under any given delivery rate 9 within the operating range of the burner and regardless of the length of the burner.

From an economic standpoint, it is desirable that the cross-sectional area of the burner pipe or manifold be varied by the provision of the removable insert because it is evident that each insert having a particular contour or profile will be adaptable over a given operating range. If it is desired to change the operating range in which the burner will function efliciently the insert 24 may be removed and replaced by an insert having a different contour or profile. The contour of all burners is such that the cross-sectional area of the burner is varied longitudinally to maintain the balance between the frictional and kinetic energy forces and the replacement insert merely changes the range within which the burner will operate. Although the insert has been found to be the most economical manner of varying the cross-sectional area of the burner manifold, the invention is not to be limited to the use of an insert since it is apparent that the burner may be constructed as in Figure 9 wherein a portion of the wall of its bore has a contour or profile constructed in accordance with this invention whereby the cross-sectional area of the manifold is changed throughout its length to maintain equal pressures at all burner ports under the delivery rates within the operating range of the burner.

It will be evident that with the present invention a pipe burner may be made of any desired length without interfering with uniform flame height and resultant uniform heating. This is a decided advantage in certain commercial installations where it is not feasible to provide a plurality of short burners and obviously, overall heating efificiency is increased. The invention contemplates the design of the burner manifold with a varying crosssectional area of such size and contour that pressure-drop due to friction loss is balanced by the pressure increase due to deceleration of the flow. In this manner a substantially equal pressure is maintained at all of the burner ports to assure uniform flame height and heating. As has been previously noted, the invention also contemplates the design of the burner manifold with a varying crosssectional area of such size and contour that the pressure change is controlled in such a manner that the burner produces a desired but not necessarily uniform distribution of heat along its length. Although the burner has been illustrated as operating in a horizontal plane, said burner may be arranged to dispose the axis of the burner in a vertical plane without impairing the efliciency thereof. Further, as described herein, the invention is applied to the usual pipe burner but it is obvious that it is applicable to other types of gas burners, such as the well known type of gas conversion burner.

A burner constructed in accordance herewith may have a greatly increased length While its diameter may be held small enough to be within practical limits; the ports may be large to give increased capacity while still maintaining accurate control of the flame characteristics. Although the invention has been found most applicable to commercial gas burners, it is adaptable for use in other installations, such as for example, the steam headers in boilers and in water distribution systems.

Having described the invention, we claim:

1. A gas burner in which there is to be a uniform distribution of gas along the length thereof comprising, a body having a passage extending therethrough, said passage having a gas inlet at one end, an outlet means disposed longitudinally along substantially the entire length of the passage through which gas may escape from the passage to be ignited to form the burner flame, said passage having a length which is greater than twenty times the hydraulic radius at the inlet end, said outlet means having a combined total cross-sectional area which is greater than the cross-sectional area of the passage at its inlet end, said outlet means having the same outlet area for each unit length of the burner, means for controlling throughout the length of the passage the relationship between the frictional energy and the kinetic energy of the gas flowing through the passage to thereby control the gas pressure at all points adjacent the area of the outlet means, said last named means comprising a variation in the contour of the wall defining the passage, such variation being in accordance with the following equation:

m=hydraulic radius b and n=numerical constants representing turbulent flow conditions L=total length of passage y=distance from end remote from inlet c=a dimensionless constant representing turbulent flow conditions which is equal to approximately 1 S=density of gas mixture Qinlet=ql1al1tlty per unit of time of total gas flowing into passage t=dynamic viscosity of gas mixture 2. A gas burner in which there is to be a uniform distribution of gas along the length thereof comprising, a body having a passage extending therethrough, said passage having a gas inlet at one end, an outlet means disposed longitudinally along substantially the entire length of the passage through which gas may escape from the passage to be ignited to form the burner flame, said passage having a length which is greater than twenty times the hydraulic radius at the inlet end, said outlet means having a combined total cross-sectional area which is greater than the cross-sectional area of the passage at its inlet end, said outlet means having the same, outlet area for each unit length of the burner, means for controlling throughout the length of the passage the relationship between the frictional energy and the kinetic energy of the gas flowing through the passage to thereby control the gas pressure at all points adjacent the area of the outlet means, said last named means comprising a variation in the contour of the wall defining the passage, such variation being in accordance with the following equation:

and other portions of the passage being varied in accordance with the following equation:

1 4 ct TL m=m,..... g

where m=hy lraulic radius I m nnez=hydraulic radius at inlet end y=distance from end remote from inlet L=total length of passage H c=a dimensionless constant representing fiow conditions which is equal to /2 for streamline fiow and approximately 1 for turbulent flow t=dynarnic viscosity of gas mixture 10 S=density of gas mixture Q m1et=quantity per unit of time of total gas mixture flowing into passage References Cited in the file of this patent UNITED STATES PATENTS Hequernbourg July 22, 1881 Clarnond Dec. 12, 1905 Schneider Sept. 25, 1917 Hardel Mar. 28, 1922 FOREIGN PATENTS Great Britain of 1886 France of 1903 

